Derivations of the motion equations

[mateomy]

Practicing the derivations of the Motion Equations, and I am looking through my notes that I transcribed from my professor...Im getting caught up on one spot.

Im getting all the equations to "pop out" except for this last one, which, I can see; but, the algebra is throwing me off...

Finishing off with these as the fundamentals to get the last derivation:

$$x=v_0 + at ; t= \frac{v-v_0}{a} ; x=x_0 + v_0 t + \frac{1}{2}at^2$$

Substituting the new t value into the latter equation and expanding...

$$x= x_0 + \frac{v_0 v}{a} - \frac{v_0^2}{a} + \frac{v^2}{2a} - \frac{v_0^2}{2a} - \frac{v_0 v}{a}$$

I can't seem to get the fractions to add and subtract out in the right way so that I can get the final equation of

$$x= x_0 + \frac{1}{2a}(v^2 - v_0^2)$$

Specifically I can't get the -v(initial)^2/a and the -v(initial)^2/2a to add up so that I can factor (in the final equation) out the 1/2. I know I am doing something absent minded. Can somebody please point it out? Thank you in advance for any pointers.

 

[clementc]

try not to skip steps =P it makes it really easy to make mistakes with signs

 

[Doc Al]

$$x= x_0 + \frac{v_0 v}{a} - \frac{v_0^2}{a} + \frac{v^2}{2a} - \frac{v_0^2}{2a} - \frac{v_0 v}{a}$$

Looks like you messed up the expansion of the t² term. (You have an extra minus sign on one of the terms.)

 

[mateomy]

Looks like you messed up the expansion of the t² term. (You have an extra minus sign on one of the terms.)

Okay, I'll recheck that expansion. Thanks!